There is significant interest in the models for production of short gamma-ray bursts. Until now, the number of known short gamma-ray bursts with multi-wavelength afterglows has been small. While the {it Fermi} Gamma-Ray Burst Monitor detects many gamma-ray bursts relative to the Neil Gehrels {it Swift} Observatory, the large localization regions makes the search for counterparts difficult. With the Zwicky Transient Facility recently achieving first light, it is now fruitful to use its combination of depth ($m_textrm{AB} sim 20.6$), field of view ($approx$ 47 square degrees), and survey cadence (every $sim 3$ days) to perform Target of Opportunity observations. We demonstrate this capability on GRB 180523B, which was recently announced by the {it Fermi} Gamma-Ray Burst Monitor as a short gamma-ray burst. ZTF imaged $approx$ 2900,square degrees of the localization region, resulting in the coverage of 61.6,% of the enclosed probability over 2 nights to a depth of $m_textrm{AB} sim 20.5$. We characterized 14 previously unidentified transients, and none were found to be consistent with a short gamma-ray burst counterpart. This search with the Zwicky Transient Facility shows it is an efficient camera for searching for coarsely-localized short gamma-ray burst and gravitational-wave counterparts, allowing for a sensitive search with minimal interruption to its nominal cadence.
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